Browsing by Author "Dhandapani, Prasantha Bharathi"

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Citation - WoS: 11
Analysis of Dengue Transmission Dynamic Model by Stability and Hopf Bifurcation with Two-Time Delays
(Imr Press, 2023) Murugadoss, Prakash Raj; Baleanu, Dumitru; Ambalarajan, Venkatesh; Sivakumar, Vinoth; Dhandapani, Prasantha Bharathi; Baleanu, Dumitru; 56389; Matematik
Background: Mathematical models reflecting the epidemiological dynamics of dengue infection have been discovered dating back to 1970. The four serotypes (DENV-1 to DENV-4) that cause dengue fever are antigenically related but different viruses that are transmitted by mosquitoes. It is a significant global public health issue since 2.5 billion individuals are at risk of contracting the virus. Methods: The purpose of this study is to carefully examine the transmission of dengue with a time delay. A dengue transmission dynamic model with two delays, the standard incidence, loss of immunity, recovery from infectiousness, and partial protection of the human population was developed. Results: Both endemic equilibrium and illness-free equilibrium were examined in terms of the stability theory of delay differential equations. As long as the basic reproduction number (R0) is less than unity, the illness-free equilibrium is locally asymptotically stable; however, when R0 exceeds unity, the equilibrium becomes unstable. The existence of Hopf bifurcation with delay as a bifurcation parameter and the conditions for endemic equilibrium stability were examined. To validate the theoretical results, numerical simulations were done. Conclusions: The length of the time delay in the dengue transmission epidemic model has no effect on the stability of the illness-free equilibrium. Regardless, Hopf bifurcation may occur depending on how much the delay impacts the stability of the underlying equilibrium. This mathematical modelling is effective for providing qualitative evaluations for the recovery of a huge population of afflicted community members with a time delay.
Citation - WoS: 2
Citation - Scopus: 2
Analysis of time delay model for drug therapy on HIV dynamics
(Univ Tabriz, 2021) Sivakumar, Vinoth; Baleanu, Dumitru; Baleanu, Dumitru; Thippan, Jayakumar; Dhandapani, Prasantha Bharathi; 56389; Matematik
We present and investigate the delayed model of HIV infection for drug therapy. The stability of the equilibrium states, disease free and infected equilibrium states are derived and the existence of Hopf bifurcation analysis is studied. We show that the system is asymptotically stable and the stability is lost in a range due to length of the delay, then Hopf bifurcation occurs when tau exceeds the critical value. At last numerical simulations are provided to verify the theoretical results.
Citation - WoS: 10
Citation - Scopus: 10
Fuzzy Type RK4 Solutions to Fuzzy Hybrid Retarded Delay Differential Equations
(Frontiers Media Sa, 2019) Dhandapani, Prasantha Bharathi; Baleanu, Dumitru; Baleanu, Dumitru; Thippan, Jayakumar; Sivakumar, Vinoth; 56389; Matematik
This paper constructs the numerical solution of particular type of differential equations called fuzzy hybrid retarded delay-differential equations using the method of Runge-Kutta for fourth order. The concept of fuzzy number, hybrid-differential equations, and delay-differential equations binds together to form our equations. An example following the algorithm is presented to understand the Concept of fuzzy hybrid retarded delay-differential equations and its accuracy is discussed in terms of decimal places for easy understanding of laymen.
Citation - WoS: 14
Citation - Scopus: 15
New fuzzy fractional epidemic model involving death population
(Tech Science Press, 2021) Dhandapani, Prasantha Bharathi; Baleanu, Dumitru; Baleanu, Dumitru; Thippan, Jayakumar; Sivakumar, Vinoth; 56389; Matematik
In this research, we propose a new change in classical epidemic models by including the change in the rate of death in the overall population. The existing models like Susceptible-Infected-Recovered (SIR) and Susceptible-Infected-Recovered-Susceptible (SIRS) include the death rate as one of the parameters to estimate the change in susceptible, infected and recovered populations. Actually, because of the deficiencies in immunity, even the ordinary flu could cause death. If people's disease resistance is strong, then serious diseases may not result in mortalities. The classical model always assumes a closed system where there is no new birth or death, no immigration or emigration, while in reality, such assumptions are not realistic. Moreover, the classical epidemic model does not report the change in population due to death caused by a disease. With this study, we try to incorporate the rate of change in the population of death caused by a disease, where the model is framed to reduce the curve of death along with the susceptible and infected populations. Since the rate of change turned out to be very small, we have tried to estimate it fractionally. Thus, the model is defined using fuzzy logic and is solved by two different methods: a Laplace Adomian decomposition method (LADM) and a differential transform method (DTM) for an arbitrary order alpha. To test its accuracy, we compared the results of both DTM and LADM with the fourth-order Runge-Kutta method (RKM-4) at alpha=1.
Citation - WoS: 7
Citation - Scopus: 7
On a novel fuzzy fractional retarded delay epidemic model
(Amer inst Mathematical Sciences-aims, 2022) Dhandapani, Prasantha Bharathi; Baleanu, Dumitru; Thippan, Jayakumar; Baleanu, Dumitru; Sivakumar, Vinoth; 56389; Matematik
The traditional compartmental epidemic models such as SIR, SIRS, SEW consider mortality rate as a parameter to evaluate the population changes in susceptible, infected, recovered, and exposed. We present a modern model where population changes in mortality are also considered as the parameter. The existing models in epidemiology always construct a system of the closed medium in which they assume that new birth, as well as new death, will not be possible. But in real life, such a concept will not be assumed to not exist. From our wide observation, we find that the changing rate in every population case is notably negligible, That's why we are preferring to calculate them fractionally using FFDE. Using Lofti's fuzzy concept we are picturing the models after that we are estimating their non-integer values using three distinct methodologies LADM-4, DTM-4 for arbitrary fractional-order alpha(i), and RKM-4. At alpha(i) = 1, comparison of the estimations will be done. In addition to the simulation, works of numerical estimations, the existence of steady states, equilibrium points, and stability analysis are all done.
Citation - WoS: 14
On stiff, fuzzy IRD-14 day average transmission model of COVID-19 pandemic disease
(Amer inst Mathematical Sciences-aims, 2020) Dhandapani, Prasantha Bharathi; Baleanu, Dumitru; Baleanu, Dumitru; Thippan, Jayakumar; Sivakumar, Vinoth; 56389; Matematik
COVID-19, a new pandemic disease is becoming one of the major threats for surviving. Many new models are arrived to study the disease mathematically. Here we are introducing a new model in which instead of studying a day by day changes we are studying the average of 14 day transmission because its life or the patients incubation period is about an average of 14 days. Also, since this is pandemic, and being not aware of susceptible population among the world's population, we considered the model without S-susceptible population. i.e., IRD- Infectious, Recovered, Deathmodel. In this new model, we are also introducing a new method of calculating new number called N0-average transmission number. This is used to study the average spread of infection instead of basic reproduction number R-0. The motto of this paper is not to predict the daily cases but to control the current spread of disease and deaths by identifying the threshold number, exceeding which will increase the spread of infection and number of deaths due to this pandemic. Also if the 14 day average IRD-populations are maintained under this threshold number, will definitely control this pandemic disease globally. Stability analysis and test for sti ff system of di fferential equations are studied. Our main aim is to present the medical world, a threshold population of infected, recovered and death cases for every average of 14 days to quickly overcome this pandemic disease COVID-19.
Citation - WoS: 10
Citation - Scopus: 15
On the decomposition and analysis of novel simultaneous SEIQR epidemic model
(Amer inst Mathematical Sciences-aims, 2023) Umapathy, Kalpana; Baleanu, Dumitru; Palanivelu, Balaganesan; Jayaraj, Renuka; Baleanu, Dumitru; Dhandapani, Prasantha Bharathi; 56389; Matematik
In this manuscript, we are proposing a new kind of modified Susceptible Exposed Infected Quarantined Recovered model (SEIQR) with some assumed data. The novelty imposed here in the study is that we are studying simultaneously SIR, SEIR, SIQR, and SEQR pandemic models with the same data unchanged as the SEIQR model. We are taking this model a step ahead by using a non-helpful transition because it was mostly skipped in the literature. All sorts of features that are essential to study the models, such as basic reproduction number, stability analysis, and numerical simulations have been examined for this modified model with other models.